Frequency-domain gravitational waves from non-precessing black-hole binaries. II. A phenomenological model for the advanced detector era

TL;DR

This work introduces PhenomD, a frequency-domain IMR waveform model for aligned-spin BBHs calibrated to NR hybrids up to $q=18$ and spins $|a/m|\sim 0.85$, and extends its applicability to the Advanced LIGO/AdV era. The model is built in three frequency regions, with Region I using an uncalibrated SEOBv2 inspiral, Region II driven by NR data for merger-ringdown, and a careful mapping of 17 phenomenological coefficients to physical parameters $(\eta,\hat{\chi})$ to describe the full IMR signal. Across calibration and verification hybrids, PhenomD achieves typical mismatches $\lesssim 1\%$, confirming its suitability for GW searches and parameter estimation within its calibration region, while highlighting the necessity for more high-spin NR simulations to extend accuracy further. The paper also compares PhenomD to SEOBNRv2_ROM, showing agreement within calibration regions but potential disagreements outside them, especially at high spins, and argues for improved NR coverage in the high-spin, unequal-mass sector. Overall, PhenomD represents a robust, modular, and fast waveform family for Advanced LIGO/Virgo analyses and lays groundwork for future extensions to precessing systems (PhenomP) and broader parameter regimens.

Abstract

We present a new frequency-domain phenomenological model of the gravitational-wave signal from the inspiral, merger and ringdown of non-precessing (aligned-spin) black-hole binaries. The model is calibrated to 19 hybrid effective-one-body--numerical-relativity waveforms up to mass ratios of 1:18 and black-hole spins of $|a/m| \sim 0.85$ ($0.98$ for equal-mass systems). The inspiral part of the model consists of an extension of frequency-domain post-Newtonian expressions, using higher-order terms fit to the hybrids. The merger-ringdown is based on a phenomenological ansatz that has been significantly improved over previous models. The model exhibits mismatches of typically less than 1\% against all 19 calibration hybrids, and an additional 29 verification hybrids, which provide strong evidence that, over the calibration region, the model is sufficiently accurate for all relevant gravitational-wave astronomy applications with the Advanced LIGO and Virgo detectors. Beyond the calibration region the model produces physically reasonable results, although we recommend caution in assuming that \emph{any} merger-ringdown waveform model is accurate outside its calibration region. As an example, we note that an alternative non-precessing model, SEOBNRv2 (calibrated up to spins of only 0.5 for unequal-mass systems), exhibits mismatch errors of up to 10\% for high spins outside its calibration region. We conclude that waveform models would benefit most from a larger number of numerical-relativity simulations of high-aligned-spin unequal-mass binaries.

Figures (22)

• Figure 1: Parameter space over which the PhenomD model has been calibrated. The locations in parameter space of the calibration waveforms are indicated by red points. Also shown are the calibration points for the SEOBNRv2 (green) and PhenomC (blue) models.
• Figure 2: Mismatch error due to numerical resolution, for the $q=4$, $\chi_1 = \chi_2 = \hat{\chi} = 0.75$ (black lines) and non-spinnning $q=18$ simulations (orange lines). The solid black line shows the mismatch between waveform $q=4$ 112- and 96-point simuations, and the dashed black line shows the mismatch between the 96- and 80-point simulations. For the $q=18$ configuration, the solid orange line shows the mismatch between the 144- and 120-point simulations, and the dashed orange line shows the mismatch between the 144- and 96-point simulations (see text).
• Figure 3: Mismatch errors due to finite-radius waveform extraction for the 120-point simulations of the same $q=4$ case as in Fig. \ref{['fig:q4q18resolutions']}. Mismatches are between the $R_{ex} = 100\,M$ waveform and those extracted at $R_{ex} = \{50, 60, 70, 80, 90\}\,M$ (from top to bottom).
• Figure 4: Phase derivative $-\phi'(f) \equiv - \partial \phi(f) / \partial f$ (upper panel) and amplitude (lower panel) for the $q=1$, $\chi_1 = \chi_2 = -0.95$ configuration. The frequency ranges that were used in the fits for each section are shown as black double-ended arrows. For reference, the frequency $Mf=0.018$ is marked with a black dashed line. Shaded regions illustrate the boundaries between the different regions when constructing the full IMR waveform. The ringdown frequency for this case is $Mf=0.071$.
• Figure 5: Phase derivative $\phi'(f)$ for the $q=1$, $\chi_1 = \chi_2 = -0.95$ configuration. The numerical data (dotted) show a distinctive extremum at the ringdown frequency, $M f_{\rm RD} = 0.071$, indicated by a vertical dashed line. A fit that follows an approach similar to that used for PhenomC (dashed) is only a crude approximation to the phase for $f > f_{\rm RD}$, whereas the approach used for the PhenomD model (solid) accurately models the phase into the ringdown.